Abstract

Talking about legged locomotion often evokes the idea that animals using such devices are perfectly adapted to this kind of motion and should be copied by robotics. The aim of this contribution is to show that the evolution of legs comes late in phylogeny, be it in arthropods or vertebrates. Neural control of legs in vertebrates has to deal with conservative arrangements ‘invented’ for axial locomotion of metameric organisms. The structure of this paper is to show the importance of axial driven propulsion in vertebrates without legs, with legs and only at the end how limbs move the body in eutherian mammals.

1. Introduction

People always have admired nature for its perfection, and for hundreds of years they have tried to copy it. Today, many concepts are based on ‘learning from nature’. Biomimicry, where the mechanical properties and control architectures in animals are more or less copied, or bionics (sensu Nachtigall) or biomimetics (sensu Vincent), where the biological structures are rebuilt in technical devices are only two examples of such concepts. ‘Biologically inspired’ constructions are the more moderate approach. The idea behind these concepts is that design modifications of natural structures are totally induced by their function—a simplistic view of adaptation. While technical structures can be and are designed de novo, biological structures always are the result of a past, permanent and ongoing historical process (‘derived’ from ancestors). They are carrying their special evolutionary burden, and by mere logic their adaptation can only be perfect if the past and recent functional requirements are identical, which under the logically necessary prerequisite of a constant environment might even be more an exception than the rule. Actually, an organism should ‘fulfil’ only the absolute necessity of adaptation, to keep the highest possible degree of flexibility to react to changing environments. The heuristic problem also is that we can only observe the fact of being adapted and not the process of adaptation or the potential to adapt. Seilacher (1970) drew a triangle in which he named the ‘three vertices’: ‘historisch-phylogenetischer Aspekt’, ‘oekologisch-adaptiver Aspekt’ and ‘bautechnischer Aspekt’. Gould (2002) called ‘these idealized end-members’ ‘historical’, ‘functional’ and ‘structural’ (p. 1052), and the whole thing an ‘adaptive triangle’. ‘Structural’ includes two aspects: first, the ‘immediate and deterministic consequences of the physical properties of matter and the dynamical nature of forces’ (Gould 2002, p. 1054), a view which since D’ Arcy Thompson is familiar to all morphologists. The second aspect is the ‘spandrels of San Marco’ (Gould & Lewontin 1979), which has been introduced into biology to point to features arising by non-adaptive processes, or as simple consequences of design and growth criteria (technical architecture). Adaptation in its proper sense is therefore restricted to the functional vertex. The Seilacher triangle is a method to analyse a biological structure or any kind of biological feature attempting to hypothetically place it into the triangle (Seilacher 1970). It is immediately evident that only a-historical and a-structural features can match the functional vertex. So, why should engineers and especially biorobotics people learn from a discipline in which any feature is a compromise that tends to fulfil functional demands, but is highly constrained by two superable properties? Any biorobotic effort can only benefit from the principles derived from biology, such as the Cruse Rules on insect's kinematics and control of leg movements. In many cases, the actual biorobotics principles may be abstracted in such a way that it really does not resemble the animal precisely. ‘That is, we do not constrain ourselves to do things exactly like the animal does, but rather simply capture the principles that are found in the animal’ (Ritzmann et al. 2004). Current attempts of construction theory aim to underlay this strategy by ‘Bionic Algorithms’ (Schilling et al. 2005). This paper advances in three steps: trunk, trunk with legs and legs with trunk. It reviews some major steps in the evolution of the vertebrate motion system and tries to illustrate why an understanding of the segmented nature of the trunk is important for an understanding of, for example, the conservative basic neural rhythmic control and its importance for axial movements. A large part will be dedicated to legged locomotion and emancipation of legs as the main motor devices in therian mammals. Aspects, which we consider to be textbook knowledge, are not especially sourced (see also Fischer 1998, 2003; Fischer et al. 2002; Fischer & Witte 2004; Fischer & Blickhan 2006).

2. A word on metameric organization

It is of great importance for our considerations, that metamerism evolved independently within the two major branches of bilaterian organisms in fundamentally different ways (figure 1). Both arthropods and vertebrates start with segmented trunks and in both cases, segmental or metameric organization could be the prerequisite for the evolution of appendages, and finally legs.

Cladogram of Eukaryota showing the two major branches of bilaterian organisms. In each of the two branches segmental or metameric organization evolved independently (light grey) and legs occur only in a later step (dark grey).

Already in Amphioxus, the sister group or closest relative of vertebrates, as well as in basal vertebrates, the musculature is ordered in a strictly repeating, serial or myomere pattern. The origin of these myomeres are somites, i.e. mesoderm blocks which are condensed mesenchymal tissue on both sides of the notochord as is explained in many textbooks. In Amphioxus, half a somite length relocates the somites. Innervation of muscles and the muscular notochord is totally different from vertebrates, no spinal nerves occur but depolarization takes place at cytoplasmatic ‘tails’ of the muscle cells.

In vertebrates, somites form not only the body muscles (myotome) but also the axial skeleton (sklerotome) and part of the skin (dermatome). Here, the skeletal parts are relocated to allow an intersegmental attachment of the muscles. Innervation is by segmental spinal nerves with two roots, the dorsal one entering the epaxonic and the ventral one, the hypaxonic musculature. The strict segmental nature of myomeres in the trunk muscles of fishes is a principle of ordering the trunk during ontogenesis and only then transformed into polysegmental, multi-innervated muscle units in tetrapods. Nevertheless, the epaxonic musculature (roughly the hand broad muscles left and right of the spine in humans) remains segmented throughout the vertebrate history (figure 2). The rest of the muscles (hypaxonic musculature) are now organized in layers, and also the muscles of the extremities are derived from hypaxonic lateral body wall muscles.

Major steps of the evolution of body axis in vertebrates with respect to the main mode of locomotion, preferred axial motion, regionalization and organization of axial musculature. Epaxial and hypaxial musculature are indicated by light and dark greys.

3. Mechanics of terrestrial locomotion

(a) Axial locomotion drives the vertebrate trunk

Motion systems determine the overall shape of a vertebrate's body. Undulation of the body stem (head, neck, trunk and tail) is the dominant mode of locomotion in all primarily aquatic vertebrates: ‘axial locomotion’. Lateral undulation persists in terrestrial locomotion of (legged) tetrapods like salamander, and many amniotes like lizards and snakes. Principally, tetrapods use rhythmic movements of the body stem with its axial skeleton and legged locomotion strategies in parallel.

Strangely enough, the vertebrate history starts without vertebrae. Basal vertebrates still have a notochord, inherited from their chordate ancestors. A notochord persists in many fish groups like sturgeons, and even the most prominent fish, the lobe-finned Latimeria, has an extremely strong liquid-filled notochord (figure 3). The function of a notochord is simply to guarantee constant length of the body and to translate the mutual contraction of the longitudinal muscles in lateral undulation.

Chorda dorsalis of Latimeria chalumnae, next to lungfishes, the closest relative of tetrapods. Preparation at the Phyletisches Museum at Jena. Photograph courtesy of Prof. Dr Alexander Haas (Hamburg).

Vertebrae gradually replace the notochord, but also coexist in many groups. Concurrently, the spine is more and more regionalized which impacts on locomotion. The spine of fishes is regionalized more functionally than structurally; the only clear-cut regions are trunk and tail. The obligatory travelling wave along the whole body to drive vortices during aquatic locomotion (cf. Blickhan 1993) can be restricted to defined regions, while others remain rigid and have an option to develop in a proper way. In 1926, Breder developed a whole classification system according to the degree of body length involved in locomotion (for extension of this system, see Lindsey 1978). Since buoyant forces counteract gravity, antagonism of contractile actors called muscles may be symmetric around either axis. Appendices like fins may be odd in number and must not occur in pairs. Isotropic physical environmental conditions do not drive the development towards preferred directions and task sharing of functional elements.

(b) In early terrestrial tetrapods, legs primarily form thrust bearings for the lateral undulation of the trunk

A profound restructuring of the spine took place with the transition to terrestrial environments. Gravitational load inducing anisotropic mechanical conditions has such a fundamental impact on locomotion that not only limbs evolved, first as mere anchors to support lateral undulation, but also the shoulder and pelvic girdle directly or indirectly got fixed to the spine. The body hanging in between the sprawled limbs and the gravitation acting at right angle to the direction of propulsion provokes a necessity to prevent the body from ventral distraction and dorsal compression, leading to an asymmetry in the share of function between skeleton and musculature. The spine of terrestrial tetrapods is further regionalized in a more mobile cervical region and a distinct head articulation, thoracic/lumbar region, and sacral plus tail region. Only in amniotes (reptiles, birds and mammals) the cervical region really forms a neck. This is licensed by a new breathing mechanism, since due to mobile ribs these groups aspire whereas amphibians swallow air. Aspiration permits a longer tracheal pathway. Mainly the rib-free regions such as cervical and lumbar vertebrae only occur in therian mammals (marsupials and placental mammals).

(c) Legs in therian mammals carry the trunk and become adaptive elements

The trunk of therian mammals shows systematic deformation in all three rotatory degrees of freedom depending on the locomotion mode, in terrestrial locomotion, the gait. Spinal movements are the effect of small intervertebral movements adding up to what is called ‘pelvic movements’ (we have to keep in mind that mobility within the iliosacral joint is irrelevant). At symmetrical gaits, the pelvis follows a complex three-dimensional trajectory combining rotations using all the three degrees of freedom (Jenkins & Camazine 1977). ‘In-phase gaits’, such as half-bound, bound or gallop make an extensive use of the sagittal bending of the spine. In-phase gaits seem to have evolved in the stem lineage of therians, i.e. with the transition from sprawled to parasagittal limbs (see §3d) in early mammalian evolution (after the split-off of monotremes), therians introduced a new repertoire of gaits. Additive sagittal flexions and extensions take place between the last 7±1 presacral vertebrae. This leads to a particularly pronounced sagittal displacement of the pelvis. During in-phase gaits, the main contribution to step length comes from the sagittal bending: 50% in the pika, 40–60% hyrax, ca 45% tree shrew (Fischer et al. 2002). Hypotheses for the ‘invention’ of in-phase gaits were among others: elastic energy storage, increases in stride length and increase in stability. Hackert et al. (2006b) present a new approach: the ‘CoM-Shifting-Hypothesis’ which is intimately linked to the angle of attack of the forelimb (angle at the moment of touch down) and serves self-stabilization (the underlying physical concept in detail is explained by Blickhan et al. (2006)). Basic observation of this hypothesis is that the centre of mass (CoM) is always in the prolongation of the lower arm (Hackert et al. 2006a). CoM is shifted horizontally ca 10% of the body length as a consequence of spinal flexion, and by this CoM remains in the prolongation line of the ulna despite the deformation of the back, demonstrating the strong coordination between the motion of limbs and trunk. Seyfarth et al. (2003) demonstrated how the pre-stance limb retraction at the end of the swing phase might enhance the stability–behaviour of the spring-mass systems. It also tunes the values of the angle of attack and the instant of touch down. The angle of attack more and more turns out to be one of the crucial points of coordination in locomotion. This might be one reason for the high conformity of touch down angles in various only distinctly related mammalian groups.

(d) Leg design in tetrapods

Limbs are held in a sprawled position during standing and also during locomotion in all tetrapods, except bipedal birds, humans and quadruped therian mammals. Locomotion is driven by body stem undulation, with the appendages used to anchor the body's propulsion at the ground or in slow walking gaits by a kind of pushing and crawling. The ‘irrelevance’ of legs for tetrapod locomotion is demonstrated by the fact that limbs are secondarily lost in several groups like limbless amphibians or blindworms, which are not snakes.

In sprawlers, humerus and femur are held almost horizontal and at about right angles to the long axis of the body. During locomotion, the distal limb describes a large horizontal ellipse with respect to the shoulder and hip joint. A step of the hind limb is realized by a combination of limb excursion and lateral undulation of the trunk. In the forelimb, an additional contribution of the shoulder girdle by gliding the latter in a sternal ridge has been observed (Jenkins & Goslow 1983; Lilje & Fischer 2004).

The evolution of mammalian limbs is marked by the transition from a two-segmented, sprawled tetrapod limb to a three-segmented limb (Kuznetsov 1995; Fischer 1999; Fischer & Blickhan 2006). The addition of functionally motional active segments on the fore and hind limbs is achieved in different ways: a pivotable shoulder blade is added as a proximal third long segment to the ‘old’ forelimb, whereas on the hind limb the existing distal element, tarsus+metatarsus is elongated and becomes the third segment, articulated to the rest of the leg by the ‘new’ ankle joint. As a consequence, serial homologous elements such as humerus and femur correspond to each other phylogenetically but not functionally. Based on orientation and configuration, the new functional correspondence now is: shoulder blade with thigh, upper arm with lower limb and forearm with foot. These postural changes are intertwined with the behaviour of the limbs during locomotion.

The new posture of the therian mammalian body meets the varying mechanical demands of locomotion in different ways than in sprawlers. The basic requirement for all animals is to cope with uneven terrain, in which the touch down position cannot be fixed and often not even be anticipated. In order to avoid vertical fluctuations of the CoM, dynamic stability in therians is achieved by a clear separation of the propulsive proximal from the stabilizing and adjusting (‘fine tuning’) distal segments (shock absorber). The legs are compliant and not just inverted pendula. The gain of all these dramatic changes in postcranial construction is not speed but endurance.

It can be expected that self-stability also plays a massive role in complex gaits such as galloping, where complicated interactions with the animal's trunk come into play. Based on models derived for phylogentically ‘young’ species like humans or horses, a first promising study on the ‘old’ mammal Ochotona rufescens (pika; Hackert 2002) revealed that the virtual front limbs in a small mammal model extending from the point of contact of the individual foot to the CoM of the animal can be treated as two springs, decelerating the body in sequence (figure 4). Self-stability can be achieved, provided the two limbs maintain a certain sequence and use a suitable angle of attack. Moreover, bending of the trunk provides a retraction movement of the forelimbs enhancing the range of stability like predicted by Seyfarth et al. (2003).

Small mammals model for the angle of attack β of forelimbs. The angle connects the point of touch down and the CoM. θ is the delay between trailing and leading limb (from Hackert et al. 2006b).

The kinematic consequences of the reorganization of the postcranial apparatus are the first different position of the forelimb's pivot, which now lies at the superior border of the shoulder blade. One simple rule of limb joint contribution to step length is that higher the share is, more proximal their pivots are. Therefore, this position assigns to the scapula the dominant role in forelimb propulsion (Fischer et al. 2002). In general, half to more than two-thirds of forelimb stance length (distance from foot down to foot up) is due to scapular rotation and translation (movement along the thorax) independently of the gaits. Hence, we face the curious situation that the main propulsion of the forelimb is not executed in a joint in the classic sense of anatomy, because the scapula's point of rotation (its superior border) is only held and guided by muscles, which show a specific evolution from sprawled mammals (monotremes) to therians with parasagittal limbs. The principal joint of the forelimb is force controlled! This is well in line with the observation that in humans the main joint of the extremities providing the first (and here only) ground contact, the hip joint, underlies strict control of the direction of the resultant force (Witte et al. 1998). It is also important to note that in eutherian quadrupeds, the pivots of the forelimb and the hind limb (hip joint) are exactly on the same distance from the ground.

Basic kinematics of tri-segmented, continuously flexed limbs of therian mammals are as follows.

Pivots of the scapula and hip joint are at the same level at symmetrical gaits and therefore fore and hind limbs have the same functional length.

Progression is mainly due to the action of proximal segments (forelimb: always scapula, hind limb: femur at symmetrical gaits and lower spine at in-phase gaits).

Distal limb joints do telescoping work compensating for external disturbances.

Two segments (scapula/lower arm, femur/metatarsus) operate in matched motion during retroversion of the limb (‘pantograph behaviour’).

Orientation of segments parallel to the ground at the beginning or at the end of stance phase in order to exploit their maximum length in smaller therians.

Position of forelimb touch down just below the eye with the exception of primates, which possess elongated upper and lower arms except for small primates.

Uniform forelimb configuration at touch down and highly similar angle of attack.

The therian zigzag-shaped, parasagittal limbs are highly sensible to loading. In the moment of touch down gravity induces flexion in the joints. Muscle–tendon complexes acting as actuator spring complexes compensate torques imposed by gravity in order to achieve equilibrium. These anti-gravity, anti-flexor muscles are usually called extensors (Goslow et al. 1981; Fischer 1994, 1998). Inverse dynamical analysis of the locomotion of small mammals shows that vertical force determines the magnitude of torque in their joints while acceleration or deceleration only modulates the occurrence of muscle moment maxima (Witte et al. 2002a,b). Torque patterns of fore and hind limbs are congruent with the observed prevailing activity of extensor muscle or muscle groups such as supraspinous, triceps brachii and quadriceps femoris or triceps surae. Such biarticular muscles (except supraspinous) mainly counterbalance gravity (cf. Jacobs et al. 1993; van Ingen Schenau et al. 1995).

4. Control of the vertebrate motion systems

(a) Central pattern generators

Coordination and synchronization of movements of different body parts are the fundamentals of any movement, be it locomotion or ‘idiomotion’ (non-locomotory movements directed towards the animal itself, for example, cleaning or congeners). Neuronal networks residing in the central nervous system control rhythmic, cyclic movements as well as acyclic autonomous and voluntary movements. Neuronal oscillators providing a spatiotemporal pattern of motor neuron and hence muscular activity generate rhythms. The core of such oscillatory networks is known as central pattern generator (CPG). In the last 50 years, a high number of experiments and studies were performed to gain insight into the mechanisms of CPGs, and how the proper coordination of different CPGs and motor neuron pools is guaranteed, especially during complex spatiotemporal movement pattern in limbed animals. Grillner (1975) proposed independent CPGs for flexor and extensor muscle groups for limb segments and each single limb. Until now, the real neuronal circuit, which makes up a CPG, has not been demonstrated in limbed vertebrates. Nevertheless, the spinal segments, hosting the oscillating circuits, could be shown in spinal preparations. In the rat and mouse neonatal spinal cord, CPGs are placed both in the cranial spinal cord (C7, C8, Th1) and in the lumbosacral spinal cord. Each CPG spinal region exhibits its own oscillatory frequency, but could entrain the rostral or/and caudal segments, respectively.

Work on the lamprey has elucidated the structure and function of CPGs and the rostrocaudal gradient of excitation and led to impressive computer simulations (Ekeberg & Grillner 1999). Although the real neuronal circuit of a CPG has not yet been demonstrated in the limbed vertebrates (tetrapods), Ijspeert (2001) has succeeded to simulate a salamander during undulation and legged locomotion, thus the hypothetical basis for action of CPGs during legged locomotion has become more clear (http://lslwww.epfl.ch/birg). As a side remark, Ijspeert mentions that a salamander when running fast returns to exclusive undulatory locomotion like in its swimming mode (comparable with that of a lamprey).

The evolution of limbs entails a reorganization of the ventral root spinal nerves into two plexus, one for each pair of legs. The amount of segments contributing to these plexus and the complexity of their pathways increases within the tetrapods and especially from mammals with sprawled posture (monotremes) to those with parasagittal limbs (therian mammals; Koizumi & Sakai 1997). The decisive neural step allowing the legs to take over the leading role in locomotion is the development of new corticospinal pathways or better highways. The supraspinal descending projections that influence distal limb muscles are the rubrospinal and corticospinal tracts. The former is found in other vertebrates but the corticospinal tract is observed only in mammals. The direct connection of fibres of the corticospinal tracts, which usually synapse on motor neurons or interneurons that ultimately go to distal limb muscles. It is probably the prerequisite for the compliance of the distal limb during locomotion, timed by long single whisker hairs and their follicle sinus complexes at the wrist and ankle joints (G. Klauer 2005, personal communication).

5. Human locomotion

Accepting that anthropogenesis is and has to be in continuity with this evolutionary process of development, it should not be surprising that human locomotion is founded on the aforementioned principles—which from the historical perspective of humans may be named ‘basic’—and that for specialization during the last 6 000 000 years only relatively small modifications have to be discussed, in comparison with the fundamental changes described for some 140 000 000 years of evolution of therians.

Indeed, locomotion is guided or even driven by motions of the trunk like in all other vertebrates, and analysis of human locomotion should be started from this point of view. The obvious phenomenon of rhythmic deformation of the human trunk during locomotion, described, for example, by Thurston & Harris (1983) or Inman et al. (1981), only just recently has been shown to occur systematically (Witte et al. 2004). Yet unpublished results of a consecutive study show the twisting of the trunk during walking to occur in comparable amount around longitudinal (torsion) and sagittal (lateral tilt) axes, dominated by gait frequency, showing rather fixed phase relations, while the amplitudes of rations show typical resonance phenomena in dependence of speed, centred around a relative minimum at the ‘energetically optimal velocity’ corresponding to Cavagna et al. (1977). In contrast to this observation, twice the gait frequency, showing smaller, more fluctuating amplitudes and no simple dependence of amplitude and phase relation from gait velocity dominate sagittal flexion and extension.

Those trunk motions may be dominated by the need of guiding the CoM in a potential field formed by gravity and elasticity of hip muscles (this hypothesis may be derived from the observations of Tardieu 1990a,b; Tardieu et al. 1993), or it may serve the placement of the CoM relative to the point of ground contact; in either case, legs and arms have to be looked at as servants of the trunk. Extremities have to mediate between the task to carry the trunk through potential fields and the boundary conditions offered by the environment. They have to provide ground contact in phase-correct timing with trunk motion and have to be able to sustain force and torque reactions of the substrate—which mainly are provoked by gravity, which overrides inertial forces by far. To realize this task under the restriction of minimized energy expenditure, resonance mechanisms seem to be used intensely. Mass concentration on legs and arms near the trunk (Hildebrand 1985) not only indicates minimization of mass moments of inertia, maximizing acceleration per torque, but also allows for long steps with high frequencies (for the morphofunctional consequences in humans cf. Witte et al. 1991). The legs and arms may not be simple suspended pendula as stated by Weber & Weber (1836) or Braune & Fischer (1895)—nature is not fighting against pendulum properties but makes use of them even if this is in a complex manner (Hoy & Zernicke 1985; Kubo et al. 2004). For the stance phase, the inverted pendulum model proposed by Mochon & McMahon (1980a,b) has to be extended by additional springs to a resonant systems (figure 5), fitting to the needs of self-stabilization (Seyfarth et al. 2001).

The inverted pendulum model of human bipedal walking extended by additional springs to a resonant system.

Just recently it has been shown that the linear properties of the ankle spring, determined by Weiss et al. (1988) in a quasi-static approach, during stance change: after a period of linear spring behaviour around heel contact the ankle spring during stance becomes progressive, to change to an energy source in push off (H. Herr 2005, personal communication). Nevertheless surprisingly, the overall linear spring behaviour of human legs is linear (Blickhan & Full 1993), and the interference of mass distribution and mechanics of locomotion seems to follow simple principles: minimization of torques using resonant counter-movements and adapted mass-distribution. The overall human body shape may be explained by simple mechanical models (Witte et al. 1991 and consecutive work), and thus simple design rules for anthropofunctional robots may be defined even if we do not understand human locomotion in detail yet (Witte et al. 2004). Perhaps, a new unified model theory for walking and running will allow a breakout (http://www.lauflabor.de/, based on Blickhan (1989) and Geyer et al. (2005)).

6. Outlook

Beneath the aforementioned methodological approaches to drive the development of standardized strategies, ‘algorithms’ for a bionic or biomimetic transfer from life sciences into the technical field, from an engineering perspective the approach of Full & Koditschek (1999) towards a common theory of motion seems promising. General ‘templates’ mathematically described in physical models form a common platform, on which life scientists analytically search for ‘anchors’ (or ‘embodiments’ sensu Pfeifer) in the real living world, while engineers synthesize their ideas by anchoring the templates in constructions. This approach should make the old insight of mathematics being the common language of scientists and becoming useful for the interaction of natural and engineering sciences.

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Interactions between motions of the trunk and the angle of attack of the forelimbs in synchronous gaits of the pika (Ochoctona rufescens). In Adaptive motion of animals and machinesKimuraH, TsuchiyaK, IshiguroA, WitteH2006app. 69–77. Eds. Berlin, Germany; New York, NY:Springer.